Simplify the following expression: $ z = \dfrac{r + 4}{9r - 4} + \dfrac{-6}{5} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{r + 4}{9r - 4} \times \dfrac{5}{5} = \dfrac{5r + 20}{45r - 20} $ Multiply the second expression by $\dfrac{9r - 4}{9r - 4}$ $ \dfrac{-6}{5} \times \dfrac{9r - 4}{9r - 4} = \dfrac{-54r + 24}{45r - 20} $ Therefore $ z = \dfrac{5r + 20}{45r - 20} + \dfrac{-54r + 24}{45r - 20} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{5r + 20 - 54r + 24}{45r - 20} $ $z = \dfrac{-49r + 44}{45r - 20}$